Question

I have a (k x n) matrix. I have initially managed to linearly regress (using the lm function) column 1 with each and every other column and extracted only the coefficients.

fore.choose <- matrix(0, 1, NCOL(assets))
for(i in seq(1, NCOL(assets), 1))
{

  abc <- lm(assets[,1]~assets[,i])$coefficients
  fore.choose[1,i] <- abc[2:length(abc)]

}

The coefficients are placed in the fore.choose matrix.

What I now need to do is to linearly regress column 2 with each and every other column, and then column 3 and so on and so forth and extract only the coefficients.

The output will be a square matrix of OLS univariate coefficients. Kind of similar to a correlation matrix, but it is the beta coefficients I am interested in.

fore.choose <- matrix(0, 1, NCOL(assets))

will initially need to become

fore.choose <- matrix(0, NCOL(assets), NCOL(assets))

Answer 1

I’d just compute the coefficients directly from the correlation matrix, using beta = cor(x,y)*sd(x)/sd(y), like this:

# set up some sample data
set.seed(1)
d <- matrix(rnorm(50), ncol=5)

# get the coefficients
s <- apply(d, 2, sd)
cor(d)*outer(s, s, "/")

You could also use lsfit to get the coefficients of one term on all the others at once and then only have one loop to do:

sapply(1:ncol(d), function(i) {
  coef(lsfit(d[,i], d))[2,]
})